How can I make a looping animation when dealing with random particles?
Faking a Looping Particle System

One possibility is to have your particle system use many particles moving very quickly, render it, and then cut off the beginning of the rendered animation in a video editing app. Here is an example:



In this short looping video clip, the starting position of the particles does not match the ending position, so it's not a perfect loop, but by having lots of particles moving quickly, the viewer is much less likely to notice this break in the continuity.

Then again, my computer is very slow, so it's possible the poor quality of playback I get hides the break in continuity -- maybe on a faster computer, it'd be too obvious, I don't know.